> * Rates of smoking in Belarus are also high.
Russia and Poland have higher rates of smoking. Anyway, it would be mostly about lung cancer which isn't the main component here.
> * The indirect impact of Chernobyl includes a lack of health care facilities in the (rural) regions most impacted.
Lack of healthcare facilities doesn't really impact cancer incidence rate.
>If the stat you're working from was breast cancer mortality, I'd push back harder, but I don't think that's what you're saying.
Breast cancer incidence rate is the main component here. It shows the largest increase in absolute terms. Thyroid cancer shows largest percentage increase, though it is "just" a 1K of cases. Geographically correlates with fallout too.
So far i really fail to see how any argument you've put forward can explain such a significant and regionally (Mogilev and Gomel are large regions, so it is not some local effect) regionally correlated increase in the cancer rate. Especially given that those regions received several Hiroshimas worth of fallout which explains that increase perfectly.
So your explanation need to be at least as good as the Chernobyl fallout provides. Specifically any such explanation has to account for the observed size of the rate increase as well as its geographical distribution, i.e. it should clearly answer - "why Gomel and Mogilev?"